Orthonormal basis for spline signal spaces
M. KAMADA, Kazuo Toraichi, Yasuhiko Ikebe, Ryoichi Mori · International Journal of Systems Science · 1989
A system of functions is derived which constitutes an orthonormal basis for the signal space composed of spline functions and whose shapes are analogous to those of Fourier's orthonormal functions. Characteristics of the orthonormal basis are analyzed in comparison with Fourier's. This gives a foundation to the use of spline functions in signal processing for signal approximation and interpolation. The orthonormal basis is different from Fourierapos;s in the sense that its Fourier coefficients are not zero up to higher frequencies, but it is similar to Fourierapos;s in the sense that its Fourier coefficients attenuate rapidly. The orthonormal basis derived introduces a concept analogous to harmonic frequency into the signal space of spline functions and the best approximating signal is obtained by evaluating inner products.